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DOKUZ EYLÜL UNIVERSITY
GRADUATE SCHOOL OF NATURAL AND APPLIED
SCIENCES
SHUNT VOLTAGE REGULATION OF SELF-
EXCITED INDUCTION GENERATOR
By
Changiz SALIMIKORDKANDI
October 2012
İZMİR
SHUNT VOLTAGE REGULATION OF SELF-
EXCITED INDUCTION GENERATOR
A Thesis Submitted to the
Graduate School of Natural and Applied Sciences of Dokuz Eylül
University In Partial Fulfillment of the Requirements for the Degree
of Master of Science in Electric and Electronic Engineering
by
Changiz SALIMIKORDKANDI
October 2012
İZMİR
iii
Acknowledgements
I would like to express my sincere gratitude and appreciation to my supervisor
Assist.Prof.Dr. Tolga SÜRGEVIL for his guidance and fruitful discussions.
I would like to thank to Prof.Dr. Eyüp AKPINAR for his encouragement and
recommendations.
I also sincerely thank to my parents, Ebadollah and Nahid, for providing
continuous guidance and support throughout the project.
Changiz Salimikordkandi
iv
SHUNT VOLTAGE REGULATION OF SELF-EXCITED INDUCTION
GENERATOR
ABSTRACT
In this thesis, the excitation methods for stand-alone self-excited induction
generator (SEIG) using fixed capacitor bank, voltage source inverter (VSI) and static
synchronous compensator (STATCOM) are presented. The steady-state analyses of
the SEIG with fixed capacitor excitation for constant frequency and constant speed
operation are performed in MATLAB environment. Stand-alone SEIG’s dynamic
characteristics are examined using the simulation models in stationary reference
frame based on q-d reference frame theory. In order to verify the machine models, an
experimental setup of SEIG with fixed capacitor bank was built in the laboratory.
The results obtained from steady-state and dynamic model of the induction machine
are compared by the laboratory tests results. The shunt voltage regulator schemes for
stand-alone SEIG based on VSI and STATCOM under constant speed and variable
load conditions are studied. The performances of these regulation schemes are
examined through simulations in MATLAB/Simulink using the developed models
for this purpose.
Keywords: Induction generator, self-excitation, voltage regulation, STATCOM,
VSI, dynamic modeling.
v
KENDİNDEN UYARTIMLI ENDÜKSİYON JENETATÖRÜNÜN ŞÖNT
GERİLİM REGÜLASYONU
ÖZ
Bu tez çalışmasında, sabit kondansatörlü, gerilim kaynaklı evirici (VSI) ve statik
senkron kompansatör (STATCOM) kullanarak bağımsız kendinden uyartımlı
endüksiyon jeneratörü (SEIG) için uyartım metotları sunulmuştur. Sabit kondansatör
uyartımlı jeneratörün sürekli-hal analizleri, sabit frekans ve sabit hız için MATLAB
ortamında gerçekleştirilmiştir. SEIG’ in dinamik karakteristikleri q-d referans
çerçevesi teorisine dayalı durağan referans çerçevesinde oluşturulan benzetim
modelleri kullanılarak incelenmiştir. Makina modellerini doğrulamak için sabit
kondansatörlü SEIG deney düzeneği laboratuarda kurulmuştur. Endüksiyon
makinasının sürekli-hal ve dinamik modelinden elde edilen sonuçlar laboratuar test
sonuçları ile karşılaştırılmıştır. SEIG için VSI ve STATCOM kullanan şönt gerilim
düzenleyici dizgelerinin çalışması sabit hızda ve değişken yük koşulları altında
incelenmiştir. Bu gerilim düzenleyici dizgelerin performansı bu amaç için
MATLAB/Simulink' te oluşturulan modeller kullanılarak incelenmiştir.
Anahtar sözcükler: Endüksiyon jeneratörü, kendinden uyartım, gerilim
regulasyonu, STATCOM, VSI, dinamik modelleme.
vi
CONTENTS
Page
THESIS EXAMINATION RESULT FORM ............................................................. ii
ACKNOWLEDGEMENTS ....................................................................................... iii
ABSTRACT ............................................................................................................... iv
ÖZ ............................................................................................................................... v
CHAPTER ONE - INTRODUCTION……………………...………………...…....1
CHAPTER TWO - LITERATURE SURVEY ON INDUCTION
GENERATORS……………………………………………….....……………..……3
2.1 Self Excitation Process………………………………………..………....…….5
2.2 Excitation Methods ……………………………………………………..……..7
2.2.1 Excitation by Capacitor Bank …………………………………………....7
2.2.2 Excitation by Controlled Rectifier………………………..…….....……..8
2.2.3Excitation by Capacitor Bank and Controlled Rectifier……….……….....9
2.2.4 Excitation by SVC and STATCOM ……………………………....…....10
CHAPTER THREE-STEADY STATE ANALYSIS OF FIXED CAPACITOR
STAND-ALONE SELF-EXCITED INDUCTION ENERATOR……………….12
3.1 Per-Phase Equivalent Circuit of Self Excited Induction Generator (SEIG)
Excited by Fixed Shunt Capacitor………………………….……….……….12
3.2 Operation Condition of Stand-Alone SEIG………………………………….15
3.2.1 Constant Frequency Operation………………..…………………..…….15
3.2.2 Constant Speed Operation ………………………………………....…..18
3.3 Comparison of Analysis and Experimental Results …………………..……20
3.3.1 No-Load Characteristics of Induction Machine…………....…….……..21
3.3.2 Constant Frequency Operation Results………………………………....22
3.3.3 Constant Speed Operation Results……………………………………....24
vii
CHAPTER FOUR - DYNAMICAL MODEL OF INDUCTION MACHINE....29
4.1 Dynamical Model of Three Phase Induction Machine ………………….....29
4.1.1 Voltage Equations in qd0 Reference Frame…………………………...31
4.1.2 Modeling of Induction Machine in the Stationary Reference Frame.....34
4.1.3 Saturation Model……………………………...………………………..37
4.2 Simulation Model of Induction Motor in MATLAB/SIMULINK……….....40
4.2.1Comparison of Simulation and Experimental Results of Induction
Motor.......................................................................................................43
4.3Dynamical Model of Fixed Capacitor Self-Excited Induction
Generator.....................................................................................…….…....…45
4.3.1 Comparison of Simulation Results with Experimental and Steady-State
Analysis Results of SEIG…………………………………...……..…...47
4.3.1.1 Voltage Buildup Under No-Load…………………………...……48
4.3.1.2 Load Variation after Full Excitation………………………….....50
CHAPTER FIVE - VOLTAGE REGULATION OF STAND ALONE SELF
EXCITED INDUCTION GENERATOR……………………………...…………51
5.1 Voltage Regulation by using Variable Capacitor Bank……………………..51
5.1.1 Simulation Model of Voltage Regulation by Variable Capacitor Bank.52
5.1.2 Simulation Results of using Variable Capacitor Bank………………....53
5.2 Regulation of the Generated Voltage by using Voltage Source Inverter…..56
5.2.1 Modeling of the VSI and dc Load ……………………………………..57
5.2.2 Simulation Model of SEIG and VSI……………………………..……..59
5.2.3 Results of Voltage Regulation by using VSI……………………...........61
5.3 Regulation of the Generated Voltage by using STATCOM………………...65
5.3.1 Modeling of the Connected ac Load and STATCOM ………………...66
5.3.2 Simulation Model of Shunt Voltage Regulation by using STATCOM....68
5.3.3 Results of Shunt Voltage Regulation by using STATCOM……….......71
5.4 Shunt Voltage Regulation using Feedback from Stator Voltage……………79
CHAPTER SIX - CONCLUSION...........................................................................80
REFERENCES...…………………………………………………….……………..85
1
CHAPTER ONE
INTRODUCTION
In the past, nearly half century ago, electricity was important but not essential.
But today, the social living has more problems such as traffic problems, no heating,
no light and communication without electricity. On the other hand, the traditional
methods to produce electricity need to consume other energy sources such as gas,
fuel, nuclear energy. By increasing cost of the gas and fuel in the past decade, the
electricity cost is increased dependently. Also, the environmental pollution problems
due to usage of these sources have led to interest in alternative energy sources such
as solar and wind energy.
The synchronous machine and induction machine can be used as a generator in
renewable energy plants. When the losses of transferring energy is an important point
to decrease cost of electricity, production of electricity in local is the other important
point of scientists’ view. When the local production is our aim, we need a machine
that doesn’t need maintenance and also it is independent from other sources like as
battery (DC source). Therefore, induction machine can be a good candidate in local
energy conversion such as in wind farms. These machines are inexpensive and
reliable, but they need an extra reactive power source to control the voltage, typically
by means of a capacitor bank at the terminals of self-excited induction generator
(SEIG). The advantages of the induction machine against synchronous machine are
well known. These are simplicity, reliability, self-protection against short circuit
faults, low cost, minimum service requirement and good efficiency. Despite these
advantages, SEIG have two major disadvantages. The magnitude and frequency of
voltage generated by SEIG will vary under variable speed, variable excitation and
variable load operation.
The objective of this thesis is to examine the methods of stator voltage control in
SEIG by using shunt regulation techniques. In this scope, capacitor excitation,
voltage source inverter (VSI) excitation and static synchronous compensator
(STATCOM) excitation methods were examined by means of computer simulations.
1
2
The results show that by using these methods, it is possible to achieve acceptable
voltage regulation on the stator terminals of the induction generator.
The studies accomplished in this thesis are summarized in the following chapters:
Chapter 2 contains a literature survey on excitation methods of the stand-alone self-
excited induction generators. In Chapter 3, the steady-state analyses of fixed
capacitor SEIG are performed for both constant speed and constant frequency
operating conditions. In order to observe the dynamic behavior of the induction
machine, its q-d reference frame model is presented in Chapter 4. In Chapter 5, the
methods of voltage control are discussed and specific control strategies are examined
through dynamic simulations. In Chapter 6, conclusions and future work are given.
3
CHAPTER TWO
LITERATURE SURVEY ON INDUCTION GENERATORS
Induction machines have some advantages when compared to other electrical
machines. These are simplicity, reliability, low cost, minimum service requirement
and good efficiency. Induction machines can be operated without needing a separate
source for supplying the rotor field current; instead, these currents are applied to the
rotor by electromagnetic induction from stator. These advantages make this machine
popular in applications as a generator in renewable energy, especially in remote
applications of wind and hydro energy (Haque, 2008). These machines absorb the
fluctuation of mechanical power delivered by the wind source. Therefore, induction
machine become a suitable generator to produce energy from the wind (Meier,
2006).
Induction generators can be classified according to the structure of rotor and
connection of the machine’s stator windings to the external electrical circuit. If the
rotor of induction generator consists of windings similar to its stator windings, it is
called wound rotor induction generator. These types of machines are more expensive
and less robust. The generator is called squirrel cage induction generator, if the rotor
has short-circuited conducting bars parallel to the generator shaft instead of
windings. Because of its being inexpensive and robust, the squirrel cage induction
generators are more common (Meier, 2006). Classification of induction generator
with respect to connection of the machine to external electrical circuit divided into
two categories. Induction generator can be connected to the electrical power grid,
which is called grid connected induction generator, which is shown in Figure 2.1. In
this mode, the machine supplies active power to the grid and absorbs reactive power
from grid. Also, both amplitude and frequency of the generated voltage will be
determined by the electrical grid (Haque, 2008; Joshi, Sandhu & Soni, 2006). It is
also possible to supply the reactive power requirement of the induction generator
locally. In this case, the machine is called stand-alone self-excited induction
generator (SEIG). This machine is able to generate voltage if the required reactive
power of machine is supplied by an appropriate capacitor bank connected to the
3
4
stator. At startup, there must be a residual voltage at the stator terminals to provide
self-excitation. The capacitor bank provides the reactive power requirement of the
machine and load, which is illustrated in Figure 2.2.
Figure 2.1 Grid Connected Induction Generator scheme
Figure 2.2 Stand-alone self-excited induction generator scheme
The advantages of SEIG are well known; ruggedness, simple structure, low cost,
self-protection against short circuit faults (Singh, 2003). Unfortunately, these
machines have some major disadvantages that restrict the application of this machine
in sensitive loads. These are large variation and deregulation of terminal voltage and
frequency under varying load conditions. (Mosaad, 2011; Singh, 2003; Sharma &
Sandhu, 2008).
In literature, there are survey studies that classify the structures and analysis
methods of self-excited induction generators (Bansal, 2005; Singh, 2003). To analyze
the induction machine in steady-state and transient, the per-phase equivalent circuit
5
and q-d models are used, respectively. In steady-state analysis, by using some
methods such as loop impedance (Ahmad & Noro, 2003; Chan & Lai, 2001; Haque,
2008; Murthy, Bhuvaneswari, Ahuja & Gao, 2010) and nodal admittance (Anagreh
& Al-Refae’e, 2003; Ahmed, Noro, Matso, Shindo & Nakaoka, 2003; Hashemnia,
Kashiha & Ansari, 2010; Ouazene & Mcpherson 1983), the performance of machine
can be analyzed. On the other hand, in transient analysis of machine, q-d model has
been extensive because it simplifies the complex equations of the machine (Krause,
2002; Ong, 1998; Wang, & Su, 1997). These analysis methods are explained in
Chapter 3 and Chapter 4 in details.
2.1 Self Excitation Process
It is well known that, by a suitable capacitor bank across the induction generator
terminals and driving the rotor at a suitable speed, voltage can be induced at the
stator windings because of the residual magnetism that initially exists in the machine.
This method is called self-excitation and in order that self-excitation occurs, the
following conditions should be satisfied:
There should be enough residual magnetism in the machine, if not, by using a
battery connected at two terminals of stator or starting the machine in
motoring case, it can be produced.
The capacitor bank across the stator terminal of machine must have a suitable
value.
The EMF induce in the induction machine due to residual magnetism initially
circulates a leading current on the capacitor and then the flux produced by this
current increase the induced EMF. As the voltage of the machine increases then the
capacitor current will also increase. As a result, the stator voltage will increase until
the generated reactive power by the capacitor bank and the reactive power consumed
by the generator are equal. The no-load terminal voltage of induction generator is
dependent on the value of capacitor curve and machine’s magnetizing curve.
Intersection of these two curves is the magnitude of generated voltage by the
6
machine at no-load (Anagreh & Al-Refae’e, 2003; Phumiphak & Uthai, 2009). This
process is illustrated in Figure 2.3. This point will be changed by any change in the
rotor speed, capacitor value and load conditions.
Figure 2.3 Voltage build-up process of SEIG
The excitation time is dependent on the values of residual magnetism and the
capacitor. Obtaining the critical and maximum value of connected capacitor is
important, because SEIG terminal voltage will collapse or no excitation will occur if
the capacitor value 1( )C is less than the critical capacitor value 2( )C as shown in
Figure 2.4. However, if the value of capacitance is selected much higher, the
operating frequency of machine will decrease. Because, by increasing the capacitor
value, magnetizing current in the machine will be increased. As the magnetizing
current increases, the copper losses on the stator will be increased. This causes an
increase in the generator slip and the frequency of the voltages will be decreased
(Anagreh & Al-Refae’e, 2003). As a result, more ohmic losses and thus less
efficiency will occur. Usually, the capacitor value is chosen to be some more than the
critical value ( 3C ) as shown in Figure 2.4 (Hashemnia, Kashiha & Ansari, 2010;
Wang & Cheng, 2000).
7
Figure 2.4 Induction generator and capacitor voltage curves
2.2 Excitation Methods
In stand-alone self-excited condition, the required reactive power is supplied from
an external circuit. Therefore, a fixed capacitor bank or other electronic controller
methods can be employed for the excitation of the generator.
2.2.1 Excitation by Capacitor Bank
The SEIG scheme with fixed capacitor excitation was shown in Figure 2.2. This
type of excitation is suitable when the load is constant and also the prime mover
provides constant speed to the rotor of the generator. Any change in the load and
speed will affect the frequency and the magnitude of the stator terminal voltage. In
the literature, a Genetic Algorithm based approach to obtain constant voltage and
constant frequency operation of SEIG was proposed where the terminal voltage
magnitude was regulated by adjusting the capacitor value and the frequency was
regulated by adjusting the rotor speed (Joshi, Sandhu & Soni, 2006).
8
To feed dc loads or regulate ac output for stand-alone or grid connected systems,
ac-dc power conversion interface is required (Wu, 2008). In order to obtain constant
frequency on the connected load, an ac-dc-ac converter can be also connected to the
stator of machine. In this case, voltage across the load is variable and constant in
frequency if this scheme shown in Figure 2.5 is used. In order to obtain constant
voltage on the stator/load terminals, the value of the capacitor bank can be changed
by using additional capacitor banks and switching these capacitors depending on any
change in the load and speed. The disadvantage of this method is that the rectifier
will generate harmonics and it may cause power resonance and noise in the machine
(Wu, 2008).
Figure 2.5 Excitation and ac/dc power conversion interface by using a fixed capacitor bank
2.2.2 Excitation by Controlled Rectifier
In this method, the VSI supplies active power to the dc load and the reactive
power required by SEIG. Hence, the power capability of VSI is large, and it
increases the cost and loss (Hazra & Sensarma, 2010; Jayaramaiah & Fernandes,
2006). This method is illustrated in Figure 2.6. The simulation model is built and
analysis of the dynamic behavior of this method is examined in Chapter 5.
9
Figure 2.6 Excitation and control of terminal voltage by using VSI
Also, for supplying the reactive power needed by SEIG and obtaining a regulated
ac output, back to back converters that consist of a controlled rectifier and an inverter
can be used (Dastagir & Lopes, 2007). This process is illustrated in Figure 2.7. The
reactive power demand of the machine is provided by the voltage source converter
(VSC). Also, it transfers the active power generated to the load side and regulates the
dc bus voltage. Usage of voltage source inverter (VSI) allows us to supply a three
phase ac load at fixed frequency. The advantage of this method is that the machine
can be operated in variable speed and variable load conditions (Wu, 2008). The main
disadvantage of this method is that the converters have to be rated to at least rated
generator power (Dastagir & Lopes, 2007).
Figure 2.7 Excitation and control of load voltage and frequency by using ac/dc/ac power converter
interface
2.2.3 Excitation by Capacitor Bank and Controlled Rectifier
Disadvantage of previous method (cost and losses in excitation by voltage source
converter) can be handled by employing the method shown in Figure 2.8. In this
method, the amplitude and frequency of generated voltage by induction generator are
10
regulated by using back to back converters between induction generator and load.
The major reactive power that the induction generator demands is supplied by the ac
capacitor bank and the VSC supplies the fine tune reactive power depending on any
change in load and speed. In this scheme, the losses and cost of the VSC is reduced
since it supplies a portion of reactive power required by the induction generator. As a
result, cost of the system is decreased. The VSI still supplies full active power to the
load (Wu, 2008).
Figure 2.8 Excitation and control of load voltage and frequency by using AC capacitor bank and
ac/dc/ac power converter
2.2.4 Excitation by SVC and STATCOM
Excitation of the machine is not restricted by above methods. In order to excite
the machine and regulate the generated voltage by the machine, static VAR
compensator (SVC) or static synchronous compensator (STATCOM) can be used as
shown in Figure 2.9 (Ahmed & Noro, 2003; Singh, Murthy & Gupta, 2004). Using
this method, the magnitude of the terminal voltages can be maintained constant under
variable load. By controlling the reactive power supplied by STATCOM/SVC in
shunt with the SEIG. For supplying the major reactive power requirement by SEIG, a
fixed capacitor bank is used. Also, for supplying the additional reactive power
needed by the machine and load depending on conditions STATCOM or SVC is
used. In this case, the machine is able to deliver constant voltage and variable
11
frequency to the load (Kuperman & Rabinovici, 2005). This method is also examined
in Chapter 5.
Figure 2.9 Excitation and control of terminal voltage by STATCOM/SVC
12
CHAPTER THREE
STEADY STATE ANALYSIS OF FIXED CAPACITOR STAND-ALONE
SELF-EXCITED INDUCTION GENERATOR
Steady state analysis is useful to determine the operation of stand-alone SEIG and
also design and usage of this machine for appropriate application. To analyze the
stand-alone SEIG with fixed capacitor in steady-state condition, its per-phase
equivalent circuit is required. From dc test, blocked-rotor test, and no-load test, the
parameters of the equivalent circuit are obtained. The performance of machine is
calculated when the speed, excitation capacitors, and the value of load across the
stator of machine are known. To estimate the performance of the machine, loop
impedance (Ahmad & Noro, 2003; Chan & Lai, 2001; Haque, 2008; Murthy,
Bhuvaneswari, Ahuja & Gao, 2010) and nodal admittance (Anagreh & Al-Refae’e,
2003; Ahmed, Noro, Matso, Shindo & Nakaoka, 2003; Hashemnia, Kashiha &
Ansari, 2010; Ouazene & Mcpherson 1983) methods have been developed in
literature. In all these analysis methods, it is assumed that magnetizing reactance is
the only element affected by magnetic saturation and other circuit parameters are
considered as constant.
3.1 Equivalent Circuit of Self-Excited Induction Generator with Fixed Shunt
Capacitor
The per phase equivalent circuit of a three-phase SEIG with shunt excitation
capacitor and resistance load is shown in Figure 3.1. The rotor parameters are
referred to the stator of the machine.
12
13
Figure 3.1 Per-phase equivalent circuit of SEIG with fixed shunt capacitor and
resistive load
The difference between synchronous speed and rotor speed is determining the
value of slip, which can be written as
s r
s
W W a bS
W a
(3.1)
where sW is the synchronous speed, rW is the rotor speed, a is the per unit frequency
and b is speed value in per unit.
On the rotor side, substituting slip from equation (3.1) in 2R
S
2 2R aR
S a b
(3.2)
To obtain the normalized form of circuit, all parameters in Figure 3.1 are divided
by base frequency (a), which is shown in Figure 3.2.
14
Figure 3.2 Normalized equivalent circuit of SEIG
The symbols in these equivalent circuits indicate the following:
1 2,R R Stator and rotor resistance in ohms, respectively
1 2,X X Stator and rotor reactance parameters in ohms, respectively
mX Machine magnetizing reactance in ohms
1E Air gap voltage in volts at rated frequency
S Slip factor
a Per unit frequency
b Per unit speed of rotor
TV Terminal voltage in volts
R Resistance load in ohms
It must be noted that, the core loss resistance is neglected because of its large
value. In this case
2 1mI I I
(3.3)
where, 1I is the stator current, Im is the magnetizing reactance current, 2I is the rotor
branch current (Boldea, 2006; Ouazene & Mcpherson, 1983).
15
3.2 Operating Conditions of Stand-Alone SEIG
Depending on the prime mover’s control, the induction generator can be operated
in three modes. (a) Constant speed, (b) constant frequency and (c) variable speed
variable frequency (Anagreh & Al-Refae’e, 2003). In this thesis, the second order
slip equation model is used (Boldea, 2006) to analyze the machine in constant
frequency and to analyze machine in constant speed the nodal admittance method is
used (Ouazene & Mcpherson 1983).
3.2.1 Constant Frequency Operation
Constant frequency operation is shown in Figure 3.3 and can be obtained by
controlling the speed such that the frequency of the generated voltage is held
constant. In this mode of operation, the value of mX is variable depending on load
and speed, therefore, it is assumed as an unknown. The other unknown is slip (S),
when the machine is operated in constant frequency. Once mX and S are calculated,
the terminal voltage, stator current, rotor current and the performance of machine can
be calculated (Boldea, 2006; Joshi, Sandhu & Soni, 2006; Sandhu & Jain, 2008).
Figure 3.3 Constant frequency SEIG scheme
Considering a resistive load connected to the stator terminals, from equivalent
circuit given in Figure 3.1
16
2
2 2 2
cL
c
RXR
a R X
(3.4)
2
2 2 2
cL
c
aR XX
a R X
(3.5)
where L LR jX is the parallel equivalent of the load and capacitive branches
(Boldea, 2006).
Analysis of circuit at node 0 gives
1 2 0mI I I
(3.6)
Substitution of current values gives
1
1 1 2 2
1 10
m L L
SaE
jaX R jX R jSaX
(3.7)
where
1 1L LR R R 1 1L LX X X
(3.8)
Real part of equation (3.7) can be written as
1 2
2 2 2 2 2 2
1 1 2 2
0L
L L
R SR
R X R S a X
(3.9)
And the imaginary part equation (3.7) is equal to
17
2
1 2
2 2 2 2 2 2
1 1 2 2
10L
m L L
X aS X
aX R X R S a X
(3.10)
Solution of (3.9) is used to find the operating slip such that
2
1 2 3 0K S K S K
(3.11)
where
2 2
1 2 1LK a X R , 2 2
2 2 1 1L LK R R X , 2
3 1 2LK R R
(3.12)
and
2 2 1 3
1,2
1
4
2
K K K KS
K
(3.13)
Equation (3.14) provide two values of slip ( 1S and 2S ) that only the lower real one
is acceptable for generator mode. Once the slip is calculated the speed of machine
can be calculated from
1b a s
(3.14)
After obtaining the slip from equation (3.13), the magnetizing reactance can be
determined from (3.10) such that
2 2 2 2 2 2
2 2 1 1
2 2 2 2 2 2 2
1 2 2 2 1 1
( )
( ) ( )
L L
m
L L L
R S a X R XX
X R S a X aS X R X a
(3.15)
18
The no-load saturation curve that is obtained from no-load motoring operation is
used to define relation between mX and 1E , which is given in section 3.4. The
relation between mX and 1E can be written as a fifth order polynomial
5 4 3 2
1 1 2 3 4 5 6m m m m mE p X p X p X p X p X p
(3.16)
As 1, ,E S F and mX are known, the machine efficiency can be obtained (Boldea,
2006).
3.2.2 Constant Speed Operation
For steady state analysis of machine in constant speed operation mode, the
equivalent circuit given in Figure 3.2 can be used. As indicated in previous operation
mode, it is assumed that only magnetizing reactance is affected by the saturation and
also the core losses are ignored (Ouazene & Mcpherson, 1983).
For a resistive load, the combination of shunt branch, 2
cXj
a and
R
a, in per phase
equivalent circuit can be written as (Ouazene & Mcpherson, 1983).
2
2 2 2L
c
RXcR
a a R X
(3.17)
2
2 2 2L
c
R XcX
a R X
(3.18)
From nodal admittance method the three branches admittance in equivalent circuit
must be equal to zero
0s m rY Y Y
(3.19)
The real and imaginary part of equation (3.19) yields, respectively
19
21
2 22 1 2 2
1 2
0L
L L
RRR
a ba
R RX X R Xa a b
(3.20)
12
2 22 12 2
12
10
L
m
L L
X XX
X RR X X RXaa b
(3.21)
If the value of speed, load resistance and excitation capacitor are given, the two
unknowns in machine are frequency and magnetizing reactance. When the speed is
known, the only unknown is the frequency of machine and it can be calculated from
real part of total admittance. From equation (3.20), the following expression can be
written as a fifth order polynomial
5 4 3 2
5 4 3 2 1 0 0Q a Q a Q a Q a Q a Q
(3.22)
Where 0 5Q Q are functions of equivalent circuit parameters, which are expressed as
230 2 ( )
RQ bR
R
(3.23)
2 2 2 23 2 21 2 3 3( ) ( ) ( )
R R XQ R R b R
R R R
(3.24)
2 2 22 1 1 12 3 22 ( ) [( ) ( ) 2( )]
c c
X R X XQ bR bR
R X R X
(3.25)
2 2 2 2 2 21 1 l 2 2 23 2 3 1 1
X R X X R X [ ( ) +( ) -2 ( )]+R ( ) +R ( ) +b R ( )
c c c c
Q RR X X R X X
(3.26)
2 21 25 2 1
X X ( ) +R ( )
c c
Q RX X
(3.27)
20
224 5 1
X[Q +R ( ) ]
c
Q bX
(3.28)
where
3 1R R R (3.29)
Equation (3.22) can be solved in MATLAB program by root command. The roots
of this equation are imaginary and real, but only the real roots are acceptable in
practice (Ouazene & Mcpherson, 1983).
After calculating the machine operating frequency, magnetizing reactance can be
determined from equation (3.21) by following equation: (Ouazene & Mcpherson,
1983)
2212
2 11 2
L
m
L L
RR X a b
aX
R RX X X R
a b a
(3.30)
And similar to the constant frequency operation, the value of air gap voltage can be
obtained from equation (3.16). The values of p1- p6 are obtained from no-load curve
of induction machine tested in the laboratory and results are given in the next section.
3.3 Comparison of Analysis and Experimental Results
Steady-state analysis and experimental results of SEIG with a resistive load
between infinite and 160 ohm are compared in this section. The test machine is a 1.1
kW, 4-pole, 400-V, 50/60-Hz, Y-connected squirrel-cage induction machine having a
rated current of 2.8 A. From dc test, blocked-rotor test, and no-load test the circuit
parameters of the machine are calculated and shown in Table 3.1. The value of each
capacitor in the Y-connected excitation capacitor bank is 30μF.
21
Table 3.1 1.1 kW induction machine parameters obtained from tests
Rs Ω X1 Ω R2 Ω X2 Ω Xm Ω Xm-uns Ω
7.9 8.1 8.2 8.1 96.5 140
3.3.1 No-load Characteristics of Induction Machine
By applying variable voltage to the stator terminals of the machine at rated
frequency (50 Hz), the no load characteristics of the machine can be obtained. In
above condition, according to slip concept, its value will be very small (in practice it
is assumed zero), and with respect to the rotor equation 22
RjX
S , this branch can be
assumed as an open circuit. Therefore, by measuring the applied voltage to the stator
of machine and stator current that is approximately equal to the magnetizing current,
saturation curve of machine can be obtained ( 1E Versus mI ). The no-load curve
obtained in experimental setup and 30 µF capacitor voltage line are shown in Figure
3.4, where the interaction of two curves determine the generator terminal (line - to -
line) voltage at steady-state and no-load.
Figure 3.4 Capacitor and no-load curves of SEIG
From curve fitting tool (CFTOOL) in MATLAB, a fifth order polynomial can be
determined to obtain the value of mX versus 1E , which is illustrated in Figure 3.5.
22
Figure 3.5 Magnetizing reactance (Ω) versus air gap voltage (V)
With the experimental test data that are fitted to a 5th order polynomial, the
following polynomial coefficients are obtained:
p1 =-2.443e-008;
p2 = 1.613e-005;
p3 =-0.0042;
p4 =0.5139;
p5 =-30.29;
p6 =927.9;
3.3.2 Constant Frequency Operation Results
Constant frequency operation is implemented by changing the machine’s rotor
speed to obtain constant frequency on the laboratory setup. In this test the stator
voltage, stator current, load current, frequency and rotor speed had measured. The
experimental results are shown in Table 3.2. Also the machine steady state analysis
results and comparison between these two results (experimental and simulation) are
shown in Table 3.3 and Figure 3.6, respectively.
23
Table 3.2 Experimental results of constant frequency operation
Load
(Ω)
Stator
Voltage (V)
Stator
Current (A)
Load Current
(A)
Stator
Frequency
(HZ)
Rotor Speed
(RPM)
∞ 228 2.25 0 50 1500
384 211 2.15 0.55 50 1524
288 205 2.15 0.71 50 1536
192 190 2.14 0.98 50 1560
160 175 2.06 1.09 50 1575
Table 3.3 Computer analysis results of constant frequency operation
Load
(Ω)
Stator Voltage
(V)
Stator Current
(A)
Load Current
(A)
Stator
Frequency
(HZ)
Rotor
Speed
(RPM)
∞ 228 2.2 0 50 1500
384 210 2.1 0.55 50 1546
288 204 2.1 0.7 50 1558
192 188 2.1 0.97 50 1580
160 174 2 1.08 50 1594
24
From above test, it is obvious that terminal voltage continue to decreasing by any
increasing in the load current. This procedure is illustrated in Figure 3.6. The
analysis results are almost verified by the experiments
Figure 3.6 Terminal voltage (V) of SEIG in constant frequency (Hz) operation
3.3.3 Constant Speed Operation Results
When the machine is operated in constant speed, stator frequency and voltage is
changed by load variation. Experimental and analysis results of machine in constant
speed are shown in Table 3.4 and Table 3.5, respectively.
25
Table 3.4 Experimental results of constant speed operation
Load (Ω) Stator
Voltage (V)
Stator
Current (A)
Load Current
(A)
Stator
Frequency
(HZ)
Rotor Speed
(RPM)
∞ 228 2.25 0 50 1500
384 204 2.07 0.53 49.5 1500
288 193 2 0.67 49 1500
192 164 1.78 0.85 48.1 1500
160 131 1.5 0.81 47.6 1500
Table 3.5 Computer analysis results of constant speed operation
Load
(Ω)
Stator
Voltage (V)
Stator
Current (A)
Load Current
(A)
Stator
Frequency
(HZ)
Rotor Speed
(RPM)
∞ 227 2.2 0 49.8 1500
384 197 2 0.51 49.5 1500
288 186 1.88 0.65 48.5 1500
192 157 1.67 0.8 48 1500
160 133 1.5 0.83 47.2 1500
26
Similar to the constant frequency operation mode, the terminal voltage of SEIG is
varied by any variation on the load resistance. From Figure 3.7 it could be seen that,
when the load current is increased, the generated voltage by SEIG will be decreased.
Closeness between the experimental and simulation results verify the computer
simulation.
Figure 3.7 Terminal voltage (V) versus load current (A) in constant speed operation
Figure 3.8 shows the stator frequency of SEIG, in both laboratory and computer
analysis. The stator frequency of SEIG decreased when the load current is increased.
Figure 3.9 shows the generated voltage versus load resistance values. The generated
voltage by the SEIG will be decreased by decreasing the connected resistive load. As
shown in Figure 3.7 and Figure 3.9, the terminal voltage is collapsed when the value
of the load is decreased to its critical value of 180Ω.
27
Figure 3.8 Terminal frequency (Hz) versus load current (A) in constant speed operation
Any reduction in the load will cause output power increment and terminal voltage
reduction. Figure 3.11 shows the generated voltage versus output power by changing
the connected load. From this figure, it is possible to determine the maximum
loading capacity of the generator at constant speed mode.
28
Figure 3.9 Terminal voltage (V) versus resistive load (Ω)
Figure 3.10 Variation of terminal voltage (V) versus output power (W)
29
CHAPTER FOUR
DYNAMICAL MODEL OF INDUCTION MACHINE
In this chapter, the dynamical model of induction machine in both motor under
load and generator mode with fixed excitation capacitors connected to the stator of
induction generator will be studied by using the qd0 transformation theory. State-
space dynamical model of induction machine taking magnetic saturation into account
will be presented in stationary reference frame. The induction machine model has
been built in MATLAB/SIMULINK tool and simulation results are verified by the
experiments carried out in laboratory setup.
4.1 Dynamical Model of Three Phase Induction Machine
In this modeling, the machine will be considered as a three phase induction motor
with balanced three-phase windings and direction of currents is into the terminals.
The MMF distribution in the machine is assumed to be sinusoidal. The stator
voltages in terms of resistance and inductance voltages can be written as
( )
abcsabcs s abcs
dv r i
dt
(4.1)
where , abcs abcsv i andabsc are the stator voltages, stator currents and flux linkages,
respectively, and are 3 1 vectors defined by:
as as as
abcs bs abcs bs abcs bs
cs cs cs
v i
v v i i
v i
(4.2)
Similarly, rotor voltage equations in terms of rotor variables can be written as
( )
abcrabcr r abcr
dv r i
dt
(4.3)
where , abcr abcrv i andabsr are the rotor voltages, and are 3 1 vectors defined by
29
30
ar ar ar
abcr br abcr br abcr br
cr cr cr
v i
v v i i
v i
(4.4)
Referring all quantities to the stator of the machine, flux linkage equations in
terms of the winding inductances and currents can be written as (Krause, 2002).
'
'' '
abcs abcss sr
T
sr rabcr abcr
iL L
L L i
(4.5)
where
1 1
2 2
1 1
2 2
1 1
2 2
ls ms ms ms
s ms ls ms ms
ms ms ls ms
L L L L
L L L L L
L L L L
(4.6)
'
' '
'
1 1
2 2
1 1
2 2
1 1
2 2
lr ms ms ms
r ms lr ms ms
ms ms lr ms
L L L L
L L L L L
L L L L
(4.7)
'
2 2cos cos( ) cos( )
3 3
2 2cos( ) cos cos( )
3 3
2 2cos( ) cos( ) cos
3 3
r r r
sr ms r r r
r r r
L L
(4.8)
31
where
0
(0)
t
r r rdt
(4.9)
and r is the rotor speed in electrical radians per second.
In above equations, the stator leakage and magnetizing inductance are denoted by
Lls and Lms, respectively. Llr is the leakage inductance of rotor windings. The
inductance Lms is also the amplitude of the mutual inductance between stator and
rotor windings as rotor equations are referred to the stator (Krause, 2002).
4.1.1 Voltage Equations in qd0 Reference Frame
The voltage equations of stator and rotor in abc variables, are transferred to the
arbitrary qd0 reference frame by using the following transformations (Krause, 2002).
0
qs as
ds s bs
s cs
f f
f K f
f f
(4.10)
' '
' '
' '
0
qr ar
dr r br
r cr
f f
f K f
f f
(4.11)
where the symbol f is used to represent the three phase stator and rotor variables
such as voltages, currents and flux linkages (Krause, 2002).
The transformation matrices sK and rK are
32
2 2cos cos( ) cos( )
3 3
2 2 2sin sin( ) sin( )
3 3 3
1 1 1
2 2 2
sK
(4.12)
2 2cos cos( ) cos( )
3 3
2 2 2sin sin( ) sin( )
3 3 3
1 1 1
2 2 2
rK
(4.13)
where
0( ) (0)
t
d (4.14)
and
r
(4.15)
Finally, the voltage equations in arbitrary reference frame by using the above
transformations are obtained as
qs s qs ds qsv r i p
(4.16)
ds s ds qs dsv r i p
(4.17)
' ' ' ' '( )qr r qr r dr qrv r i p
(4.18)
' ' ' ' '( )dr r dr r qr drv r i p
(4.19)
33
where the symbol p represents the derivative operator .d
dt
It must be noted that
the rotor parameters are referred to the stator side and the zero sequence equations
are omitted since the conditions in the machine are assumed to be balanced.
The flux linkages are expressed as
'
qs ls qs m qs qrL i L i i
(4.20)
'
ds ls ds m ds drL i L i i (4.21)
' ' ' '
qr lr qr m qs qrL i L i i (4.22)
' ' ' '
dr lr dr m ds drL i L i i (4.23)
where 3
2m msL L
Substituting qd
qd
b
in the equations (4.16) - (4.19), they can be written in
terms of flux linkages per second as
qs s qs ds qs
b b
pv r i
(4.24)
ds s ds qs ds
b b
pv r i
(4.25)
' ' ' ' '( )rqr r qr dr qr
b b
pv r i
(4.26)
' ' ' ' '( )rdr r dr qr dr
b b
pv r i
(4.27)
where b is the base electrical angular velocity and is the flux linkages in per
second, which are expressed as
34
'( )qs ls qs m qs qrx i x i i
(4.28)
'( )ds ls ds m ds drx i x i i
(4.29)
' ' ' '( )qr lr dr m qs qrx i x i i
(4.30)
' ' ' '( )dr lr dr m ds drx i x i i
(4.31)
By using equations (4.24) - (4.27) the q and d axis equivalent circuits can be
obtained as shown in Figure 4.1.
4.1.2 Modeling of Induction Machine in the Stationary Reference Frame
In the stationary reference frame, the speed of the rotating frame is 0 . Thus,
the voltage equations can be written as
qs s qs qs
b
pv r i
(4.32)
ds s ds ds
b
pv r i
(4.33)
' ' ' ' 'rqr r qr dr qr
b b
pv r i
(4.34)
' ' ' ' 'rdr r dr qr dr
b b
pv r i
(4.35)
(a)
35
(b)
Figure 4.1 Equivalent circuits for a three phase induction machine in arbitrary reference frame (a)
q-axis circuit and (b) d-axis circuit
From Figure 4.1, by neglecting the effects of saturation the stator and rotor flux
linkages per second can be written as (Ong, 1998).
qs ls qs mqx i
(4.36)
ds ls ds mdx i
(4.37)
qr lr qr mqx i
(4.38)
dr lr dr mdx i
(4.39)
From above equations, the stator and rotor currents can be obtained as
qs mq
qs
ls
ix
(4.40)
ds mdds
ls
ix
(4.41)
'
'
'
qr mq
qr
lr
ix
(4.42)
''
'
dr mddr
lr
ix
(4.43)
By substituting equations (4.40) – (4.43) into (4.32) – (4.35), the flux linkages per
second can be expressed as follows (Barrado, Grino & Valderrama, 2007; Ong,
1998).
36
( )sqs b qs mq qs
ls
rv dt
x
(4.44)
( )sds b ds md ds
ls
rv dt
x
(4.45)
'' ' ' '
' ( )r r
qr b qr dr mq qr
b lr
rv dt
x
(4.46)
'' ' ' '
' ( )r r
dr b dr qr md dr
b lr
rv dt
x
(4.47)
where the mutual flux in linear region is
'( )mq m qs drx i i (4.48)
'( )md m ds qrx i i
(4.49)
By substituting (4.40) – (4.43) into (4.48) and (4.49), the mutual flux linkage in q
and d axes can be written as
'
'( )
qs qr
mq M
ls lr
Xx x
(4.50)
'
'( )ds dr
md M
ls lr
Xx x
(4.51)
where
'
1 1 1 1
M m ls lrX x x x
(4.52)
Finally, the motor motion and electromagnetic torque equations of the induction
motor can be written as
rem mech damp
dJ T T T
dt
(4.53)
37
3( )
2 2em ds qs qs ds
b
pT i i
(4.54)
where
damp rT B (4.55)
and mechT is the mechanical torque applied to the shaft of the machine.
In experimental setup, the combined moment of inertia of the driving dc motor
and induction generator setup is J=0.042 kg.m2 and the friction coefficient of the
drive train is B= 0.006 Nm.s/rad. These values are used in simulations.
4.1.3 Saturation Model
Saturation of iron in induction machine affects the mutual and leakage flux. In the
analysis of the machine, the magnetizing reactance will be assumed the only affected
element by the saturation. Therefore, the main factor in induction machine analysis is
determining its magnetizing inductance (Ong, 1998).
The magnetizing inductance is obtained by the no-load motor test, by driving
induction motor speed close to synchronous speed (i.e. 0S ) and measure the
variable applied voltage and resulting stator current. Magnetizing reactance of
machine can be calculated from
g
m
m
Ex
I
(4.56)
where gE is the air gap voltage and its value will be assumed the applied voltage to
the terminal of machine and mI is the stator current when the value of slip (s) in the
rotor side is zero because the rotor rotates nearly at synchronous speed.
38
The effect of the saturation is same in both q and d axes. Therefore, by using
Figure 4.2, the reduction of flux linkages per second in q and d axes can be expressed
as (Ong, 1998).
Figure 4.2 Illustration of saturation in d-q components
sat
mq mq mq
(4.57)
sat
md md md
(4.58)
By using equations (4.50) and (4.51), the saturated value of the q and d axis
mutual flux linkage can be written as
'
'( )
qs qr mqsat
mq M
ls lr m uns
Xx x x
(4.59)
'
'( )sat ds dr md
md M
ls lr m uns
Xx x x
(4.60)
where m unsx is the value of the unsaturated magnetizing reactance.
The relationship between m and mq , md can be written from Figure 4.2,
such that
39
sat
mdmd msat
m
(4.61)
sat
mq
mq msat
m
(4.62)
2 2( ) ( )sat sat
m mq md
(4.63)
The amount of decrease in the mutual flux linkage per second ( )m due to
saturation can be determined from the saturation curve of the machine. Figure 4.3
shows the 1.1 kW induction machine’s saturation curve, which is obtained
experimentally in the laboratory. As shown in Figure 4.4, the reduction in flux
linkage per second ( )m can be determined by obtaining the difference between
saturation curve and linear air gap line (Ong, 1998). The saturation characteristics of
induction machine were obtained using the calculations below and shown in Table
4.1, which is defined as a look up table in computer simulations.
Figure 4.3 Saturation curve of the 1.1kW induction machine
_ 109151
0.72
g uns
m uns
m
Ex
I
(4.64)
40
the value of mI is equal to the stator current and is obtained from no-load test.
g uns gm E E
(4.65)
Figure 4.4 Saturation characteristics of the 1.1kW induction machine
Table 4.1 Saturation characteristics of the 1.1kW induction machine defined in the lookup table.
( )gE V
86 117 148 178 233 277 319 328 346
( )m V 0 0 0 6 10.5 18 61 91 128
4.2 Simulation Model of Induction Motor in MATLAB/SIMULINK
In order to verify the experimental results for motoring operation, the machine
model including saturation was constructed in MATLAB/SIMULINK using
equations (4.32) – (4.63). Figure 4.5 shows a complete diagram of an induction
motor in stationary reference frame. The details of main blocks are shown in Figure
41
4.6(a), 4.6(b), Figure 4.7 and Figure 4.8. Figure 4.6(a), 4.6(b) show the
implementation of equations in both q and d axis circuits of three phase induction
machine. The equations (4.40) – (4.43) and (4.44) - (4.47) are implemented in the
induction machine sub-block.
Figure 4.5 MATLAB/SIMULINK simulation model of induction motor
42
(a)
(b)
Figure 4.6 Simulation model of q and d- axis equivalent circuit
Figure 4.7 shows the simulation model of rotor of induction motor given in
equation (4.53) - (4.55). When mechT is negative the machine will be generating and
in the motoring mode it will be positive. Finally, the saturation model of induction
motor given in equations (4.57) – (4.63) is shown in Figure 4.8.
43
Figure 4.7 Simulation model of motor motion and electromagnetic torque
Figure 4.8 Simulation model of mutual flux saturation
4.2.1 Comparison of Simulation and Experimental Results of Induction Motor
In order to verify the machine model, simulation and experimental results of the
induction machine during free acceleration are compared. Figure 4.9 shows the
startup speed response of induction motor obtained from both simulation and
experimental. It can be seen from Figure 4.9 that the results in both experiment and
simulation are close. When the machine is starting in standstill, and when it is
unloaded, the simulation and experimental speed reaches to synchronous speed (1500
rpm) approximately in 0.6 sec.
44
Figure 4.9 Rotor speed (RPM) response of induction motor during free acceleration test
Figure 4.10 shows the stator current of induction motor obtained from both
simulation and experiment. It can be seen that, the value of stator current in
experiment at the transient time is higher than that of the simulation results. In the
simulations, it is assumed that the only magnetizing reactance is affected by the
saturation. However, the stator and rotor leakage reactance are also affected by the
saturation due to high currents at startup. As a result of the decrease in leakage
reactance due to saturation, the stator currents increase. It can be seen that at t=0.5
sec the machine stator current decreases to the no-load value in both simulation and
experiment.
Figure 4.10 Stator current (A) of induction motor during free acceleration test
45
4.3 Dynamical Model of Fixed Capacitor Self Excited Induction Generator
In the previous section, the induction motor had been analyzed in q-d axes and the
simulation of this machine explained. In this section, the dynamical model of self-
excited induction generator will be studied. Figure 4.11 shows the self excited
induction generator equivalent circuits in q and d axes with the capacitor and
resistive load connected to the stator of machine.
Figure 4.11 q and d axis equivalent circuits of fixed capacitor self excited induction generator
When compared to induction motor model, the differences in the SEIG model are
the rotor speed, which is determined by the prime mover and the stator voltage
equations, which are determined by the capacitor bank. In this case, the current of
capacitor and the stator terminal voltage of SEIG can be expressed by using
following equations, (Avinash & Kumar, 2006; Kishore & Kumar, 2006; Seyoum,
Grantham & Rahman, 2001):
46
( )cq qs Lqi i i
(4.66)
( )cd ds Ldi i i (4.67)
It can be seen from Figure 4.11, that the capacitor (and also load) voltages are
equal to the stator phase voltages. Therefore, the capacitor voltages can be expressed
as
1( )qs qs Lqv i i dt
C
(4.68)
1( )ds ds Ldv i i dt
C
(4.69)
Finally, the load currents are expressed as
qs
Lq
Vi
R
(4.70)
dsLd
Vi
R
(4.71)
Figure 4.12 shows the stator voltages of SEIG in q-d stationary reference frame,
which are implemented by using equations (4.69) – (4.72).
Figure 4.12 Simulation model of SEIG with fixed capacitor and load
47
Figure 4.13 shows the computer simulation model of constant-speed fixed
capacitor self-excited induction generator. The saturation curve in both motoring and
generating mode is the same.
Figure 4.13 Simulation model of self excited induction generator
4.3.1 Comparison of Simulation Results with Experimental and Steady-State
Analysis Results of SEIG
In laboratory setup, in order to drive the rotor of SEIG in constant speed, a DC
motor driven by a four quadrant dc motor drive was used. The simulation results of
SEIG voltage build-up are verified by experiment. Also, the results of dynamic
simulations are verified by the results obtained from steady-state analysis.
Table 4.2 shows the results of experiment, steady state analysis and dynamical
analysis in constant speed operating mode of SEIG. As it can be seen from this
table, all results are in close agreement with each other.
48
Table 4.2 Comparison of experimental, steady state and simulation results at constant speed operation
Operation Load (Ω) Stator Voltage (V) Load Current (A) Stator Frequency
(Hz)
Experimental
Results
∞ 230 0 50
384 200 0.52 48.9
288 190 0.66 48.6
192 157 0.82 48.1
160 131 0.81 47.6
Steady-State
Analysis Result
∞ 230 0 50
384 195 0.5 48.5
288 185 0.64 48.1
192 150 0.78 47.5
160 133 0.83 47.2
Dynamic Results
∞ 230 0 50
384 202 0.52 48.5
288 193 0.67 48.2
192 160 0.83 47.6
160 131 0.81 47.5
The stator voltage values are decreased by increasing the load. The dynamic
model’s results are closer to the experimental results.
49
4.3.1.1 Voltage Buildup under No-Load
In order to verify the dynamic performance of the machine, results of
experimental laboratory setup and simulation are compared. Excitation under no-load
process is provided by employing a three phase balanced capacitor and driving the
shaft of the machine at a constant speed by a dc motor fed from a four quadrant dc
motor drive.
Figure 4.14(a) and 4.14(b) shows the experimental and simulation results of
voltage and current build-up under no-load condition, respectively. In Figure 4.14(a),
the magnitude of the generated voltage in simulation is higher than the experimental
results. In experiments, the waveform of the generated voltage is flattened due to
saturation and contain 3rd
harmonic dominantly, therefore, there is a difference in
magnitude between the experimental and simulation results. But, in both of them, the
measured voltage in RMS is equal to 230 volts. Also, the magnitudes of stator
current in both simulation and experiment are closer as shown in Figure 4.14 (b).
When generator is driven at a constant speed (1500 rpm) and it is excited with a three
phase capacitor bank (C=30 µF), the value of generated voltage attains its steady
state value of 230 volts (RMS) at 1 sec. The magnitude and frequency of generated
voltage in both simulation and experiment are close to each other.
(a)
50
(b)
Figure 4.14 Voltage and current build up of SEIG in simulation and experiment. (a) stator
voltage (V) build-up and zoomed view (b) stator current (A) build-up and zoomed view
4.3.1.2 Load Variation after Full Excitation
When the machine’s speed is constant, any variation in the connected load
affects the terminal voltage of SEIG. In order to simulate this operation, in the first
time the machine excited under no load, then at t=1.3 sec, a 400 ohms load is
connected to the terminal of SEIG. At t=1.7 sec, by connecting a 144 ohms load to
the stator terminal of SEIG, the terminal voltage is collapsed. This process is
illustrated in figure 4.15.
Figure 4.15 Stator voltage variation under different load values
51
CHAPTER FIVE
MODELING OF VOLTAGE REGULATION METHODS FOR STAND-
ALONE SELF EXCITED INDUCTION GENERATOR
In this chapter, terminal voltage regulation methods of stand-alone SEIG are
studied through simulations. In order to regulate the voltages on the stator terminals
of SEIG, different kinds of circuits are examined. These are (a) variable capacitor
bank, (b) voltage source inverter (VSI) and (C) STATCOM. The dynamic
performances of the SEIG and controller are tested by applying load variations in
computer simulations.
5.1 Voltage Regulation by using Variable Capacitor Bank
In order to control the generated voltage on the terminal of SEIG, there is variety
of VAR generators. Some methods have been used such as connecting variable
capacitors bank in series with the connected load and the stator. Unfortunately, this
scheme limits the capability of the control (Saffar, Nho & Lipo, 1998). Also,
regulation of terminal voltage is possible by adding more capacitor bank to the stator
that is called shunt voltage regulation, as shown in Figure 5.1. This voltage
regulation method is able to generate leading reactive power. The disadvantage of
this method is step variation of the terminal voltage (Saffar, Nho & Lipo, 1998).
The control scheme is designed such that the magnitude of the generated voltage
is sensed and compared with a reference voltage. If the magnitude of the generated
voltage drops down to a specific value, the additional capacitor bank will be
switched on.
51
52
Figure 5.1 Excitation and regulation of the terminal voltage by using variable capacitor bank
5.1.1 Simulation Model of Voltage Regulation by Variable Capacitor Bank
By connecting 30 µF capacitor bank to the stator of SEIG, the generated voltage
by the machine at no-load is nearly 230 volts in RMS. By changing the resistive load
from infinite to 384 ohms, the generated voltage decreases from 230 to 202 volts. In
order to restore the terminal voltage to its original value, capacitor value must be
changed from 30 µF to 35 µF. In simulations, the load is modeled as R and RL.
Figure 5.2 shows the simulation model of voltage regulation by variable capacitor
bank implemented in MATLAB/SIMULINK.
The induction generator with saturation and capacitor excitation blocks were
explained in Chapter 4. An additional control block was built by using an If Function
and an If Action Subsystem to adjust the shunt capacitor value. For control purpose,
the magnitude of the generated voltage can be obtained from q-d components as
follows:
2 2
s qs dsV V V (5.1)
53
where sV is the peak magnitude of the terminal voltage. The controller adds suitable
capacitor bank when the magnitude of the generated voltage drops down below 290
Volts.
5.1.2 Simulation Results of using Variable Capacitor Bank
Variation of the stator frequency and terminal voltage by changing the load is
shown in Figure 5.2 and Figure 5.3, respectively. It can be seen from Figure 5.2 that
at no-load time the value of frequency is nearly 49.8 Hz. The stator frequency is
decreased to 48.5 Hz when the load value is increased to 384 ohms at t=1.3 sec.
From Figure 5.3, it can be seen that the generated voltage after connecting 384 ohms
load at t=1.3 sec is reduced to 202 volts in RMS. The proper capacitor bank (35µF) is
switched on if the magnitude of the terminal voltage drops down to the specific value
(202 in RMS). After switching on the additional capacitor bank, the value of
generated voltage attains its original value of 230 volts at 1.4 sec.
At t=1.7 sec, RL (R=288 and L=800mh) load is connected. In this case, the
reactive power demand of the load is increased. Therefore, in order to keep the
terminal voltage in a constant value the value of connected capacitor is increased to
39.5µF, that cause the generated voltage attains its original value again.
Figure 5.2 Variation of the stator frequency (Hz)
54
Figure 5.3 Stator voltage regulation of SEIG by using variable capacitor bank
Figure 5.4 shows the consumed reactive power by the SEIG and load. At no-load,
the consumed reactive power by the machine is equal to
2 22303 3 1500
106c
vQ VAR
x
(5.2)
It is well known that the consumed reactive power is increased by connecting load
to the stator terminals. By connecting 384 ohms load at t=1.3 sec, the value of
capacitor is increased to 35µF. In this case the consumed reactive power by the
system is equal to
2 22303 3 1700
93.7c
vQ VAR
x
(5.3)
The demand of RL load to the reactive power is more than the R load. In this case
by connecting a 39.5µF capacitor bank, the required reactive power by the machine
and load is supplied. The amounts of reactive power consumed by the induction
generator for the given R and RL load conditions are almost the same as shown in
Figure 5.5. The reactive power consumed by the SEIG is calculated from
3
2qs ds ds qsQ v i v i
(5.4)
55
Figure 5.4 Consumed reactive power (VAR) by SEIG under R and RL loads
At the no-load the generated active power by the machine is zero. The application
of 384 ohms load at t=1.3 sec, the generated active power by the SEIG is equal to
413 W. Also, by connecting the RL load to the stator terminals of machine, the
generated active power by the machine is reduced to 323 W. As shown in Figure 5.5.
The active power delivered by the induction generator is calculated from
0 0
32
2qs qs ds ds s sp v i v i v i
(5.5)
Figure 5.5 Generated active power (W) by SEIG under R and RL loads
56
5.2 Regulation of the Generated Voltage by using Voltage Source Inverter
In order to supply the reactive power to SEIG, a voltage source inverter (VSI) can
be connected directly to the stator of machine. Also, the VSI deliver the generated
active power by the SEIG to the connected dc load. The VSI is able to control the
amplitude and frequency of stator voltage. The responsibility of VSI in this scheme
is control the amplitude of the DC bus voltage. Figure 5.6 shows the system
configuration (Hazra & Sensarma, 2008; Hazra & Sensarma, 2010; Murthy & Ahuja,
2010).
Figure 5.6 Stator voltage regulated by using VSI-PWM
In this control scheme, in order to regulate the generated voltage by the SEIG, a
controller is designed based on control of slip speed sl . When the machine is
driven at constant speed, any variation on the dc load affects the dc capacitor voltage.
The capacitor voltage will be increased by any decrease in the connected load and
vice versa. Therefore, by comparing the dc voltage with a reference dc voltage and
using a PI controller, the dc bus voltage can be controlled by adjusting the slip of the
induction machine. By adjusting the slip of induction machine to a negative value,
the induction machine operates as a generator and supplies active power to the dc
bus. As a result, dc capacitor will be charged and voltage build-up will occur.
57
The error between the measured dc voltage and the reference dc voltage is the
input of PI controller. The PI controller output gives us a negative slip speed
command. By adding this value to the rotor speed, the frequency of inverter
excitation can be obtained. To maintain an optimum flux level in the induction
machine, the voltage per frequency ratio is kept constant. By using the obtained
frequency, we are able to calculate the voltage command to the VSI in order to
implement V/F control method, which is suitable for controlling induction machine
in motoring and generating mode (Hazra & Sensarma, 2010). Inverter command
voltage is obtained from the constant V/F ratio and reference sine waveforms are
generated from the frequency and voltage commands. Finally, inverter gate pulses
are generated by means of PWM pulse generator. In order to achieve fast excitation,
the load is connected to the dc bus after the dc bus voltage is fully build-up. The
terminal voltage regulation and voltage build-up are examined through simulation
models.
5.2.1 Modeling of the VSI and DC Load
The power circuit of the three-phase VSI is shown in Figure 5.7. The inverter
consists of six switching devices and each leg has an anti-parallel diode. The upper
side signals are shown by 1 2 3, ,S S S and the lower side signals are shown
by 1 2 3, ,S S S . The valid switch state of each branch is shown in Table 5.1 (Lee &
Ehsani, 2001; Singh, Murthy & Grupta, 2004; Shokrollah, 2006).
Figure 5.7 The scheme of SEIG voltage regulation by using VSI
58
Table 5.1 Valid switch states of three-phase PWM voltage source inverter
1S
1 1S =0
0 1S =1
2S
1 2S =0
0 2S =1
3S
1 3S =0
0 3S =1
The phase voltage of SEIG stator winding can be written as
1 1 2 3( )3
dcan dc
VV V S S S S
(5.6)
2 1 2 3( )3
dcbn dc
VV V S S S S
(5.7)
3 1 2 3( )3
dccn dc
VV V S S S S
5.8)
The transformation of variables to q-d coordinates in stationary reference frame is
given by the following expressions:
1(2 )
3q a b cf f f f
(5.9)
1( )
3d b cf f f
(5.10)
where the variable f represents quantities such as voltage, current or flux. By
substituting the equation (5.9) - (5.10) into equations (5.5) and (5.6), the q-d stator
voltage are expressed as
59
q dc qV V S (5.11)
d dc dV V S (5.12)
The DC side current is equal to
1 2 3( )dc as bs csi i S i S i S (5.13)
The dc current in stationary q-d reference frame can be written as
3( )
2dc q q d di i S i S
(5.14)
Finally, the value of capacitor voltage can be obtained from
1dc cV i dt
C
(5.15)
where the cI is the dc capacitor current and expressed as
dcc dc L dc
dc
Vi i i i
R
(5.16)
5.2.2 Simulation Model of SEIG and VSI
This model was implemented in MATLAB simulink and shown in Figure 5.8.
The VSI is connected directly to the stator terminals of SEIG and a dc load is
connected to the dc side of VSI. The reactive power requirement by the induction
machine is produced by the VSI. The computer simulation model of VSI subblock is
shown in Figure 5.9. This model is the implementation of equations (5.11) – (5.16).
The simulation model of PWM pulse generation block is shown in Figure 5.10.and
Figure 5.11 shows the dc bus voltage control block diagram.
60
Figure 5.8 MATLAB Simulink model of SEIG and VSI
Figure 5.9 Simulation model of VSI in d-q stationary reference frame
61
Figure 5.10 Simulation model of PWM pulse generation block
Figure 5.11 Simulation model dc bus voltage control
5.2.3 Results of Voltage Regulation by using VSI
Figure 5.12-Figure 5.20 show the dc bus voltage build-up, variation of the stator
voltage in steady-state, stator voltage magnitude, dc bus voltage, slip speed
command*( )sl , modulation index, generated active and consumed reactive power
by the machine in response to a change in resistive dc load, respectively. Value of the
dc capacitor is set to 1000 µF which its initial value is assumed 15 Volts,
* 560dcV volts and the gains in PI controller are 0.01ik and 3.5pk ,
respectively.
At the no-load, the generated active power by the SEIG is delivered to the dc bus
by VSI, which case the dc capacitor voltage takes its steady-state at t=1.3. Figure
62
5.13 shows the stator voltage variation. It can be seen that the terminal voltage build-
up is totally completed at t=1.3 with the dc bus voltage. This time is dependent to the
dc capacitor value, as shown in Figure 5.12. it can be seen that by connecting a 500
ohms load at t=1.5 sec, the value of the stator voltage drops nearly 4 volts, Figure
5.14 and Figure 5.15. On the other hand the value of dc bus voltage drops nearly 8
volts and slip is increased in negative side from 0 to -0.06 in order to produce more
torque in the machine, as shows in Figure 5.16 and Figure 5.17, respectively. Figure
5.18 shows the value of modulation index that is kept constant in its maximum value
(0.9). The generated active power and consumed reactive power by the SEIG is
shown in Figure 5.19 and Figure 5.20, respectively. It can be seen that the consumed
reactive power by the SEIG is increased by decreasing the load value also; the
generated active power is variable dependent to the connected load value.
Figure 5.12 DC bus voltage (V) build-up at no-load
Figure 5.13 Stator voltage (V) build-up at no-load
63
Figure 5.14 Steady-state waveform of the stator voltage (V) under 500Ω dc load
Figure 5.15 Variation of the stator voltage magnitude (V) with 500Ω dc load
Figure 5.16 DC bus voltage (V) variation from no-load to 500 ohms dc load
64
Figure 5.17 Variation of slip speed command with 500 ohms dc load
Figure 5.18 Behavior of modulation index with 500 ohms dc load
Figure 5.19 Generated active power (W) by SEIG with 500 ohms dc load
65
Figure 5.20 Consumed reactive power (VAR) by SEIG with 500 ohms dc load
5.3 Regulation of the Generated Voltage by using STATCOM
In this scheme, the ac capacitor bank across the stator is used to provide the major
reactive power requirement of SEIG and the STATCOM is used to tune the reactive
power needed by the machine and load when the machine is working in constant
speed. Various control methods have been proposed in the literature such as
instantaneous power control algorithm (Jayaramaiah & Femandes, 2008). Also, this
scheme can be used with an energy storage unit (battery bank) at the dc bus to
provide frequency and voltage regulation (Dastagir & Lopes, 2007; Lopez &
Almeida; 2006; Geng, Xu, Wu & Huang, 2011). In this thesis, slip speed control
method given in Section 5.2 is applied to STATCOM for controlling the magnitude
of the generator terminal voltage and its viability is examined by simulations. The
system configuration is shown in Figure 5.21.
66
Figure 5.21 Shunt voltage regulation by using STATCOM and slip speed control method
5.3.1 Modeling of the Connected AC Load and STATCOM
Figure 5.22 shows the shunt connection type of STATCOM. By using the state
space model, it is possible to define the STATCOM dynamics model (Jayaramaiah &
Femandes, 2006).
Figure 5.22 Shunt connection of STATCOM for terminal voltage regulation of SEIG
67
As mentioned in Section 5.2, the voltage and current expressions of three-phase
induction circuit are determined by the switching states 1 2 3, ,S S S . Referring to
Figure 5.23, the DC side current can be expressed as
1 2 3( )dc ai bi cii i S i S i S (5.17)
The dc current in stationary qd reference frame can be written as
3( )
2dc qi q di di i S i S
(5.18)
Finally, the value of capacitor voltage in the DC side can be obtained from
1dc dc
dc
v i dtC
(5.19)
The STATCOM voltage behind the filter inductance (L) in stationary q-d
reference frame can be written as
qi dc qV V S
(5.20)
di dc dV V S (5.21)
The SEIG terminal voltages and STATCOM currents are then obtained as
qi
qs qi
diV V L
dt
(5.22)
dids di
diV V L
dt
(5.23)
1( )qi qi qsi V V
L
(5.24)
1( )di di dsi V V
L
(5.25)
68
In these equations, the subscript s represents the stator variables of SEIG and i
represents the STATCOM variables. The voltage and current equations of RL load
can be expressed as
( )Lq qs L
qs L Lq L Lq Lq
L L
di V RV R i L i i
dt L L
(5.26)
( )Ld ds Lds L Ld L Ld Ld
L L
di V RV R i L i i
dt L L
(5.27)
where the subscript L represents the load variables. The current of the STATCOM
can be written as
qi qs qc Lqi i i i (5.28)
di ds dc Ldi i i i (5.29)
where the subscript C represents the shunt capacitor variables. From above
equations, the capacitor currents and capacitor voltages which are equal to the stator
terminal voltages can be expressed as (Geng, Xu, Wu & Huang, 2011)
qC qi qs Lqi i i i (5.30)
dC di ds Ldi i i i (5.31)
1qs qc qCV V i dt
C
(5.32)
1ds dc dCV V i dt
C
(5.33)
5.3.2 Simulation Model of Shunt Voltage Regulation by using STATCOM
In this model, the STATCOM is connected parallel to the stator terminals,
capacitor bank and load. The complete computer simulation model is shown in
69
Figure 5.23 and its subblocks are given in Figure 5.24 – Figure 5.28. The model is
the implementation of equations (5.17) – (5.33).
Figure 5.23 MATLAB Simulink model of SEIG and STATCOM
Figure 5.24 Simulation model of DC bus voltage in q-d stationary reference frame
70
Figure 5.25 Simulation model of STATCOM currents in q-d stationary reference frame
Figure 5.26 Simulation model of stator voltages of SEIG in q-d stationary reference frame
Figure 5.27 Simulation model of load in q-d stationary reference frame
71
Figure 5.28 Simulation model of slip regulation method
5.3.3 Results of Shunt Voltage Regulation by using STATCOM
Simulations were performed to examine the voltage control capability of the
STATCOM applied to the SEIG. In these simulations, variation of the DC link
voltage, slip speed command, stator voltage in both RMS and reference value,
consumed reactive power by the SEIG, generated reactive power by the STATCOM,
generated active power by the SEIG and the active power consumed by the
STATCOM with ac load connected to the stator of SEIG with R and RL load are
shown, respectively. The value of the dc capacitor is set to 1000 µF and the gains of
PI controller are 0.01ik and 3.5pk , respectively. Also, the value of ac capacitor
bank is set to 30µF in the simulation. The simulations are in two cases: (i) applying
resistive ac load of R=144Ω, (ii) applying RL ac load of R=100Ω and L=330mH.
Case (i) R=144 Ω
In Figure 5.29, the dc bus voltage decrease nearly 10 volts by connecting 144
ohms load when the system operates at no-load initially. By applying this load in the
absence of STATCOM the terminal voltages were collapsed as shown in Chapter 3
and Chapter 4. Figure 5.30 shows the variation of the slip speed command that is
increased by increasing load value. It can be seen that the slip speed command is
increased from -0.01 to -0.07 by increasing the load value from no-load to full-load
(144 ohms). Figure 5.31 and Figure 5.32 show the instantaneous terminal voltages
72
and their peak value, respectively. Figure 5.33 shows the instantaneous stator voltage
waveforms during the transition from no-load to full-load. Generated active power
and consumed reactive power by the SEIG are shown in Figure 5.34 and Figure 5.35,
respectively. At no-load, the generated active power is equal to zero. By applying
144 ohms load, the generated active power by the machine is increased to the rated
value (1100 W). Also, the consumed reactive power by the machine is increased
from 1500 VAR to 2100 VAR. This reactive power demanded by the machine under
load is produced by the STATCOM. Figure 5.36 shows the generated reactive power
by the STATCOM under loading conditions. The consumed active power by the
STATCOM at steady-state is approximately zero and it draws real power from the
induction machine to charge the dc capacitor as shown in Figure 5.37.
Figure 5.29 DC bus voltage (V) variation of STATCOM with 144Ω ac load
Figure 5.30 Slip speed command variation with 144Ω ac load
73
Figure 5.31 Terminal voltages (V) of SEIG with 144Ω ac load
Figure 5.32 Peak terminal voltage magnitude (V) variation with 144Ω ac load
Figure 5.33 Variation of stator voltages of SEIG during the transition from no-load to full-load
74
Figure 5.34 Generated active power (W) by the SEIG with 144Ω ac load
Figure 5.35 Consumed reactive power (VAR) by SEIG with 144Ω ac load
Figure 5.36 Generated reactive power (VAR) by the STATCOM with no-load and 144Ω load
75
Figure 5.37 The instantaneous active power (W) of STATCOM
Case (ii) R=100 Ω and L=330mH
The results of simulation for the quantities that are examined under the RL load
case are shown in Figure 5.38 – Figure 5.46. The dc bus voltage, instantaneous stator
voltages and their peak values during no-load and full-load are shown in Figure 5.38,
5.40, and 5.41, respectively. Similar to the case (i) the dc voltage drop is nearly 10
volts, because the impedance seen by the machine in case (i) and case (ii) is equal.
Variation of slip speed command is illustrated in Figure 5.39, which is lower than
case (i) because the load demand less active power while its reactive power demand
increased. By applying rated RL load to the terminals of SEIG, the reactive power
demand of the load is increased. The reactive power that is being supplied from
STATCOM is the sum of the reactive powers of the load and machine. It is more in
this case when compared to case (i) and shown in Figure 5.45.
76
Figure 5.38 DC bus voltage (V) variation with R=100 Ω and L=330mH ac load
Figure 5.39 Slip speed command variation with R=100 Ω and L=330mH ac load
Figure 5.40 Instantaneous terminal voltages of SEIG with R=100 Ω and L=330mH ac load
77
Figure 5.41 Peak terminal voltage magnitude (V) variation with R=100 Ω and L=330mH ac load
Figure 5.42 Variation of stator voltages of SEIG during the transition from no-load to full-load
Figure 5.43 Generated active power (W) by the SEIG with R=100 Ω and L=330mH ac load
78
Figure 5.44 Consumed reactive power (VAR) by SEIG with R=100 Ω and L=330mH ac load
Figure 5.45 Generated reactive power (VAR) by the STATCOM
Figure 5.46 The instantaneous active power (W) of STATCOM
79
5.4 Shunt Voltage Regulation using Feedback from Stator Voltage
In the above voltage regulation mode, in order to control the stator voltage, the dc
bus voltage was sensed. Also, it is possible to design a controller by sensing the
stator voltage. The simulation results of voltage regulation by sensing the stator
voltage is shown in Figure 5.47 and Figure 5.48. The value of the connected load is
equal to 144 ohms. The variation on the terminal voltage with the dc voltage
feedback is slightly less than with feedback from ac voltage. Both methods yield to
approximately same results with the same PI parameters.
Figure 5.47 Peak terminal voltage magnitude (V) variation of SEIG using feedback from dc
voltage
Figure 5.48 Peak terminal voltage magnitude (V) variation of SEIG using feedback from ac
voltage
80
CHAPTER SIX
CONCLUSION
In this thesis, the capability and excitation issues of the stand-alone self-excited
induction generator have been studied. In order to better understand the SEIG’s
behavior, the steady-state and dynamic analysis of the machine were accomplished
and results are compared with the experimental study. The excitation methods to
control the terminal voltage in stand-alone application were studied.
The steady-state analysis for constant frequency and constant speed was studied
in MATLAB. Dynamical modeling of the induction machine based on stationary
reference frame was explained in detail using qd0 reference frame theory. The
simulated systems in both transient and steady-state were compared by the laboratory
setup results. Comparing the experimental results with the dynamical and steady-
state results verified that the dynamical model closely characterizes the behavior of
the real machine. The terminal voltage control methods using variable capacitor
bank, VSI and STATCOM were explained through simulations in
MATLAB/Simulink. For VSI and STATCOM systems, a control scheme based on
slip speed control methodology was studied. The control task was performed by a PI
regulator, which generates the slip speed command for the induction generator. As
shown in simulation results, the controller can maintain an approximately constant
voltage at the induction generator terminal and across the dc capacitor by adjusting
the STATCOM frequency under different loading conditions. Also, STATCOM can
supply the reactive power required by the load. The applicability of this control
scheme to STATCOM system is shown by means of computer simulations. The
modeling studies that have been accomplished in this thesis can be extended to
practical implementation of the systems examined as future work.
80
81
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